Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #60 Dec 18 2024 22:34:55
%S 2,0,3,1,8,7,8,6,9,9,7,9,9,7,9,9,5,3,8,3,8,4,7,9,0,6,2,0,6,2,4,1,9,8,
%T 7,9,1,0,5,4,9,8,7,8,7,5,9,0,5,7,0,3,1,7,5,0,0,2,4,7,7,4,4,1,5,1,9,5,
%U 7,5,0,7,5,9,1,9,0,6,0,2,4,8,8,3,6,2,5,0,3,6,1,6,9,0,7,7,9,6,4,2,9,1,4,6,9
%N The rumor constant: decimal expansion of the number x defined by x*e^(2 - 2*x) = 1.
%H G. C. Greubel, <a href="/A106533/b106533.txt">Table of n, a(n) for n = 0..5000</a>
%H L. Bayon, P. Fortuny Ayuso, J. M. Grau, A. M. Oller-Marcen, M. M. Ruiz, <a href="https://arxiv.org/abs/1706.07185">The Best-or-Worst and the Postdoc problems</a>, arXiv:1706.07185 [math.PR], 2017.
%H L. Bayon, J. Grau, A. M. Oller-Marcen, M. Ruiz, P. M. Suarez, <a href="http://arxiv.org/abs/1603.03928">A variant of the Secretary Problem: the Best or the Worst</a>, arXiv preprint arXiv:1603.03928 [math.PR], 2016.
%H D. J. Daley and D. G. Kendall, <a href="http://dx.doi.org/10.1093/imamat/1.1.42">Stochastic rumours</a>, Journal of the Institute of Mathematics and Its Applications 1:42-55, 1965.
%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>.
%H José María Grau Ribas, <a href="https://arxiv.org/abs/1812.09255">A New Proof and Extension of the Odds-Theorem</a>, arXiv:1812.09255 [math.PR], 2018.
%H José María Grau Ribas, <a href="https://doi.org/10.1016/j.spl.2019.108591">An extension of the Last-Success-Problem</a>, Statistics & Probability Letters (2020) Vol. 156, 108591.
%H Brian Hayes, <a href="http://bit-player.org/wp-content/extras/bph-publications/AmSci-2005-05-Hayes-rumours.pdf ">Rumours and Errours</a>, American Scientist, Vol. 93, Nbr. 3, 2005, pp. 207-211.
%F Solution to x*exp(2 - 2*x) = 1 with x not equal to 1.
%F Equals -1/2*LambertW(-2*exp(-2)). - _Vladeta Jovovic_, May 30 2005
%F Constant c satisfies: exp(c*x)/(1-2*c) = Sum_{n>=0} (x + 2*n)^n * exp(-2*n)/n!. - _Paul D. Hanna_, Mar 12 2016
%F Equals (2-A256500)/2. - _Miko Labalan_, Dec 18 2024
%e c = 0.20318786997997995383847906206241987910549878759057031750024774...
%t RealDigits[ -ProductLog[ -2/E^2]/2, 10, 111][[1]]
%o (PARI) solve(x=0, 0.5, x*exp(2-2*x)-1) \\ _Michel Marcus_, Mar 13 2016
%Y Cf. A007456, A129506, A217900, A217910, A256500.
%K cons,nonn
%O 0,1
%A _Robert G. Wilson v_, May 03 2005